Cylindrical Bi-Planar Gradient Coil for MRI

ABSTRACT

Cylindrical bi-planar gradient coil assemblies for use in open magnetic resonance imaging, wherein each of the coil assemblies contains in sequential order (i) a circular primary coil set placed flat above a cylindrical planar substrate, (ii) cooling means, (iii) 0th and 2nd order shims, (iv) shield layers, and (v) 1st order shims. In use the gradient coil assemblies are disposed symmetrically to each other about a plane of symmetry parallel to each.

CROSS REFERENCE TO RELATED APPLICATION

This application takes priority from and claims the benefit of U.S.Utility patent application Ser. No. 10/944,080 filed on Sep. 17, 2004,which in turn takes priority from and claims the benefit of U.S.Provisional Patent Application 60/504,371 filed on Sep. 19, 2003.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention is directed to a gradient coil design andmanufacturing process for making self-shielded gradient coil sets foruse in cylindrical bi-planar open magnetic resonance imaging (MRI).

2. Description of the Related Art

Progress in MRI scanner design has taken two directions. The first hasbeen towards higher field traditional magnet systems while the secondhas been towards low field open magnet systems. By “high field” magnetsystems is meant those wherein the field strength is greater than 10,000Gauss and which require superconducting wire technology to generate themagnetic fields. “Low field” magnet systems are those in which the fieldstrength is about 5,000 Gauss and below and use permanent magnets orelectrical coils. In general, the cost of the magnetic field producingmaterial is a very strong function of the imaging volume. This is moreso the case for open magnet structures than for cylindrical magnets.Therefore, image space management is crucial.

In open MRI systems, the gradient and RF coils, which have to be placedwithin the imaging volume, take up significant space. In particular, anefficient and compact structure for stacking the gradient coil layers,which typically can take up to 20-30% of the image space in the verticaldirection, is a very important goal. Moreover, the planar extent has tobe limited as much as possible because the gradient coil must becontained within the magnet poles. The volume, size and weight of themagnets scale quadratically with the radius of the magnet. Thus thisvariation is the dominant factor that controls the cost of the magnet.Therefore, limiting the planar extent of the magnet and magnet polesshould be a primary goal of any MRI system design.

In designing open, MRI systems the traditional approach has entailedusing unshielded gradient coils and then trying to design a magnetsystem that would minimize the natural interactions between the gradientfields and magnets. Although the approach has had some success, itrestricts the scanner from performing many MRI applications,particularly those requiring the use of bipolar current waveforms todrive the gradient coils due to eddy currents and residual gradientfields from conductive surfaces and magnet materials. In contrast, thepresent invention in which shielded gradient coils are used is basedupon a systems approach that seeks to avoid all interactions between themagnet and the gradient and RF coils, thereby enabling all MRIapplications to be possible.

It has also been discovered that the performance of open MRI systems canbe further improved (and the cost lowered) by including active shims inthe shielded gradient coils. The system can achieve up to two or moreorders of magnitude improvement in magnetic field homogeneity byincluding 0th, 1st, 2nd and higher order active shims.

Furthermore, permanent magnets are heated differentially from unshieldedgradient coils causing inhomogeneities and thermal drifts in magnetmaterials. It has been determined that adding cooling means in thegradient space can alleviate this significantly. Heretofore the coolingmechanisms had taken up too much space, so that the tradeoff had notbeen considered beneficial.

The present invention utilizes a gradient coil design that includesshims and cooling mechanisms located inside the gradient coil to achievethese improvements and allow a more compact open magnet design withoutsacrificing field homogeneity and performance.

Aside from physical constraints there are also imaging requirements on agradient coil's performance that are met with the shielded gradientcoils which allow the full complement of MRI applications. The use ofshielded gradient coils that include active shims in an open MRI systemhas translated into a significant performance enhancement that combinesstable homogeneity derived from self-shielding and additional activeshim sets.

Unexpectedly, the present system has also been found to suppress theacoustic noise generated by the gradient coils. This is due to theinherent greater physical size of shielded gradient coils that combinedwith the opposing gradient fields of a shielded configuration helps tostiffen the gradient assembly and generate reduced torque effects.

The present invention is based upon a design methodology and amanufacturing process to make an open self-shielded gradient coil withthe following features and benefits:

-   -   (1) ultra-fast switching;    -   (2) full 0th, 1st, and 2nd order active shims and the capacity        to provide even 3rd, 4th, 5th or higher order active shims if        needed;    -   (3) compact physical thickness and planar extent to maximize        subject access space and minimize magnet pole face space;    -   (4) air or water cooling; and    -   (5) construction and mounting method to suppress acoustic noise        generation.

The method and manufacturing process described enhance open magnet MRIperformance substantially while providing significant cost benefits dueto the substantial reduction in the open magnet size.

SUMMARY OF THE INVENTION

The present invention is directed to a gradient coil assembly for use inmagnetic resonance imaging, said coil assembly including (i) a circularprimary coil set placed flat atop a first and second cylindrical planarsubstrate disposed symmetrically to each other about a plane of symmetryparallel to each. The primary coil set is driven by a pulsed currentsignal for generating a spatially varying magnetic field in the centralplane.

The assembly further includes a circular shield coil set for the primarycoil set placed coplanar and atop the outer surfaces of the primary coilset about the first and second cylindrical planar substrates. The shieldcoil set is driven by a pulsed current signal that is substantially 180°out-of-phase with respect to the pulsed current signal in the primarycoil set for generating a spatially varying magnetic field in adirection substantially opposite to the first spatially varying magneticfield and substantially canceling the magnetic field in a regioncylindrically outside of the outer surfaces of the shield layers.

Preferably the assembly further includes a cooling mechanism placedcoplanar and atop the primary coil set between the primary coil andshield coil sets.

Also preferably the assembly includes a set of circular correction coilscomprising the 0th, 1st, 2nd, and higher order Legendre polynomialharmonics totaling about nine or more mutually orthogonal coil sets foractively shimming the main magnetic field, placed coplanar to theprimary and shield coil sets in the cylindrical planar substratessymmetrically disposed about the planar surface. The 1st ordercorrection coil sets are placed atop the shield coil set and the 0th,2nd and higher order correction coils are placed between the primary andshield coil sets and atop the cooling mechanism. Generally the primarypatterns are denser generating the most heat so placing the coolingmechanism directly above the primaries is desirable.

The primary coil sets, the shield coil sets, the cooling mechanism andthe 0th, 1st and 2nd correction coils are supported within a pair ofcylindrical planar formers.

The primary coil set generally contain three coils each generating oneof three mutually orthogonal linearly-varying magnetic fields and theshield coil set generally contains three coils generating alinearly-varying magnetic field to substantially oppose thecomplimentary primary coil field above the shield layer surface. The0th, 1st and 2nd order correction coils are designed to have a planarcircular footprint.

The cylindrical bi-planar gradient coil assembly contains in sequentialorder (i) a circular primary coil set placed flat above a first andsecond cylindrical planar substrate disposed symmetrically to each otherabout a plane of symmetry parallel to each, (ii) cooling means, (iii)oth and 2nd order shims, (iv) shield layers, and (v) 1st order shims.

The primary coil set includes an X-primary, followed by a firstinsulating layer, then a Y-primary, a second insulating layer, and aZ-primary.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 a is a cross-sectional view of a magnetic resonance imaging (MRI)machine in accordance with the present invention.

FIG. 1 b is a top view of the MRI machine of FIG. 1 a.

FIG. 2 is a cross-sectional view of a gradient coil set showing thestacking of the elements of the gradient coil set.

FIG. 3 a shows a Z primary axial coil pattern with a circular footprint.

FIG. 3 b shows one half of an X or Y primary transverse coil patternwith a circular footprint.

FIG. 3 c shows a Z shield axial coil pattern with a circular footprint.

FIG. 3 d shows one half of an X or Y shield transverse coil pattern witha circular footprint.

FIG. 4 is a block diagram showing the key steps in the manufacturingprocess of this invention.

FIG. 5 is a top view of a cylindrical former which holds the multiplelayers of a gradient coil, serves as a means to attach the gradient coilto the magnet pole, and has recesses in transverse patterns for runningbusbars to connect the gradient coil patterns while avoiding build-up ofvertical size.

FIGS. 6 a and 6 b show two alternative cooling tube designs for use withthe cylindrical gradient coil of this invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

The magnetic resonance imaging apparatus 10 is constructed as shown inFIGS. 1 a and 1 b. It has a magnetic yoke 12 magnetically connected to amagnetic circuit arrangement comprising a pair of permanent magnetblocks 14 each attached to the surface of a pole 16, which has annularprotrusions 17 for field shaping. The magnet blocks 14 also have spacefor magnetic field gradient coil assemblies 18 and RF coil assemblies20, disposed opposite each other so as to define a gap which is used asthe imaging region. The permanent magnet blocks 14 are magneticallyconnected by the yoke 12 to generate a magnetic field in the gap. Thegap has a sufficient opening to insert a subject therein for thepurposes of obtaining tomographic images. The apparatus is specificallydesigned for magnetic resonance imaging (MRI) purposes although otherapplications that require the use of a static uniform magnetic field mayalso be performed with the system.

The insertion gap used as an imaging region, is required to have amagnetic strength greater than 0.1 T (1,000 Gauss) and a uniformity lessthan 100 ppm (parts per million) throughout to obtain images ofsufficient clarity. The imaging region is large enough to image a humanbeing and has a diameter spherical volume (DSV) of about 10 to about 50cm, preferably about cm. The DSV is critical to determining thedimensions of the gap and the diameter of the pole pieces of a suitablemagnet.

The choice of design methodology and the design innovations for theplanar open gradient coil is based on imaging requirements and physicalconstraints. The imaging requirements demand that there be minimal eddycurrent and residual magnetization production, ultra-fast switchingcapability and high gradient strengths to yield very high slew rates,and highly linear gradient fields. Physically, what is required islimiting the gradient coil stacking thickness and planar extent. Thesedemands are met by using the target field method specifically solved inpolar coordinates to allow the use of a radial envelope function, whichis the key to limiting the radial extent of the gradient coil. Moreover,this approach allows a theoretically correct solution for the shieldcoil layer similarly limited in radial extent and easily extended toshim coil designs of any order.

In the open bi-planar cylindrical systems of the present invention,axial gradients are made from a pair of identical coaxial coils disposedsymmetrically to each other about a central plane and driven withopposing currents. A highly linear, very high efficiency and lowinductance axial gradient is produced by using a Maxwell pairconfiguration. This condition is met when the coils are separated by anaxial length equal to 2a and their radii are each given by 2a/√{squareroot over (3)}, where “a” is one-half the distance between the upper andlower coils along the axial direction. Using this configuration for theprimary coil the target field method can be used to design a shield. Theresulting axial gradient is so drastically changed that the performanceis very poor. To produce a similar performance with the added shieldsrequires finding new radial distributions for the primaries, which canbe done by allowing the current densities to have more than one radialdensity distribution. Adding these degrees of freedom in the targetfield specification and using a Nelder-Mead simplex optimizationalgorithm, one can find an optimal design for the radial current densitydistributions that yields very high efficiency, linearity and lowinductance axial shielded gradients.

To save vertical space the shields are made as close as possible to theprimaries, but doing so diminishes the performance of the overallgradient. This is overcome by making the current densities, especiallyin the primaries, very dense at two or more regions. This can be seen inFIG. 3 a, a coil pattern for axial primary coils. The dense regions areobtained from the aforementioned optimization. The code generates theoptimal position, i.e. the position that yields the lowest inductance,highest strength gradient and linearity. Constructing such coils hasbeen found to be a manufacturing challenge. To avoid high resistancesand generating heat, high-pressure water-jet cutting of a copper plate(or other suitable machining technique) has been found to beparticularly suitable. Alternatively but less desirably, one could usewires. The construction method is described further below.

Furthermore, to limit the radial extent in such a tight design with veryhigh current densities the last few turns of the axial gradients in boththe primaries and the shields are reversed so they produce an oppositefield to cancel the field spill-out and provide gradient confinementwithin the magnet pole space as can be seen in FIG. 3 a. The result islower energy and lower overall inductance while achieving very highswitching speeds, i.e. about 50 to 150% gain using the same amplifiersetting. This is a novel approach in axial gradient designs andconstruction.

The shielded transverse gradients are designed by starting with thefield, inductance and energy expressed in polar coordinates to maintaina circular geometry and then incorporating a constrained minimization tokeep the energy, and hence the inductance, as small as possible butwhere the constraint points and values where optimized by theNelder-Mead optimization algorithm in which the cost function includesthe gradient efficiency, linearity and inductance. This yields anoptimal design for a chosen radial and vertical configuration. Usingthis approach, the vertical separations between primary and shield arefixed and the constraint values are chosen so the radial extents arealso fixed. Thus, for a fixed set of physical values, the designs yieldthe optimal performance for the shielded transverse gradients.

A further enhancement of the design comes from the fact that acylindrical bi-planar configuration is a more natural geometry foraxial-shielded gradients, but an inefficient one for transverse-shieldedgradients. This dichotomy is resolved by placing both the axial primaryand shield coils inside the transverse primary and shield coils. Thisentails putting both the transverse primaries and shields on the outsideof the axial primaries and shields to provide an overall betterthree-axis shielded gradient performance. Shields in general deterioratethe efficiency of the primary gradients; thus the further away they arethe better.

Using these approaches, a typical gradient coil prepared in accordancewith the present invention has yielded axial and transverse shieldedperformances with peak gradients approaching 0.15 mT/m/A, inductanceswell below 800 uH, linearity of less than +/−5% on a 30 cm DSV, andshielded performances that suppress both odd and even eddy fieldproduction to less than 1-0.1% of peak gradients in a physical spacethat contains the gradients within a 45 mm vertical height, 90 cmdiameter and gradient upper to lower axial separation of 50 cm. Thoseskilled in the art of gradient coil design and production will recognizethe optimal performance achieved in a very compact physical space, yetvery wide upper to lower gradient gap.

The use of the target field method of the present invention allows thedesign of shims of any order since the technique is an analytical one.Therefore, designs for 0th, 1st, 2nd order as well as 3rd, 4th, 5th, andeven higher Legendre polynomial shim coils are easily generated andincorporated in the gradient coils. To avoid coupling the 1st ordershims to the gradients because they are also linear or 1st order, theseshims are placed above the axial and transverse shield coil layers andall other order shims are placed in the space between the primary andshield axial and transverse coils. This saves space and optimizes thegeometric compactness of the entire assembly.

The present design contrasts with previous approaches that have beenbased on rectangular coordinates and use a Gaussian or similar taperingfunction to limit the planar extent of the primary coil. That approachsuffers for two fundamental reasons. First, the geometric footprint isnot circular and consequently not optimal. Second, it does not allow forsolving the shield layer self-consistently to obtain a shield coilsimilarly limited in planar extent.

A further advantage of the present invention is that it allowsspecifying the most linear gradient field production possible whileachieving the ultra-fast switching (by including energy minimizingconstraints) and minimal eddy current production due to shielding theprimary gradient coil layer. The shielding, minimum energy constraintsand radial limits combine to limit the field spill-out, whichconsequently result in ultra-fast switching. While the rate of switchingnormally depends upon the amplifier used with the MRI system, the lowerthe inductance and resistance, the faster gradients can be switched.Thus the present invention is capable of producing inductances of 800 uHor less with resistances well under 250 mΩ depending on the type andsize of the coil material used.

Added to the benefits derived from the invention is that it permits amanufacturing process which provides for the most efficient physicalstacking of gradient, shim and cooling layers.

The manufacturing process begins by the specific choice of former tocontain and enclose the various layers. FIG. 4 provides a summary of themanufacturing process and FIG. 5 shows a former as produced below. Theformer is part of the gradient coil assembly. It is what holdseverything together and mounts to the magnet pole faces. There aremounting holes on the outer edges of the former in addition to thealignment pinholes, which also serve as mounting holes when the entiregradient assembly has been constructed. A fiber cloth braid/weave meshpattern or other similar insulating material forms the starting base forthe former. An iron form of the appropriate dimension is used to moldthe former including the mounting and screw holes. Each fiber cloth islaid inside the mold and is potted by epoxy. When the last layer isreached a pressure mold is used to obtain a flat control surface.Furthermore, the iron mold is tapered at an angle of about 3 degrees torelease the former when the epoxy has set and the pressure mold iscompleted. The former wall thickness generally ranges from about 1 mm toabout 5 mm, preferably about 1-2 mm. The former height generally rangesfrom 30 mm-45 mm. The choice of mesh and epoxy forms a strong and rigidbase to hold the weight of the various gradient coil layers and alsodampen acoustic noise generation. Using a fiber cloth weave design andpotting with an epoxy combines the benefits of being strong yet thin andhence takes up the least amount of space.

As best seen in FIG. 5, alignment holes are preferably strategicallyplaced throughout the former during the molding process so that thegradient coils that have matching holes throughout can be aligned withthe former and to each other during the construction process. The holesare placed throughout the gradient stack such that they can be used asmounting supports to the magnet pole face to help suppress acousticnoise generation. The alignment holes alter the original path of thecurrents and in a shielded design, where the balance is very delicate,the placement of the holes is designed to have minimal impact yetsuppress acoustic noise generation as best as possible. Thus the holesare located away from the densest regions in the coil patterns. Forexample, in the axial gradient pattern of FIG. 3 a there is a lot ofspace where the reverse currents are and placing the holes in theselocations is ideal because it requires minimal rearrangement of thewires/tracks.

An important space management technique used to obtain the most compactstacking possible is by etching the gradient coils from a thin copperplate typically between 3-5 mm thickness with a circular footprint. Ahigh-pressure water-jet cutting machine is used to etch the wire tracksin the plate. Etching the wire patterns gives a lot of freedom inachieving the many optimal performance targets because the wire trackscan have variable widths that are often needed due to tight designrequirement. The etching process is so precise that it allows etching ofthe alignment and support holes in the gradient coil plates as well.

Once the plates are etched by the above process, they become loose andwire track positions can change because the whole plate structure is nolonger rigid. Two methods have been developed to overcome this problem.In the first method, tabs are left strategically throughout the etchingprocess so that etched curfs are not completely cutout but rather helpkeep the plate structure rigid. Once the plate is removed from thewater-jet machine, the empty curfs are filled with epoxy and allowed tocure so that the rigidity of the plate is now maintained by the epoxyfill. Subsequently, the tabs are removed so adjacent wire tracks are notshorted to each other. In this way, the wire track positions are keptintact.

Alternatively, curf paths are molded into place using an insulatingmaterial that has a thin flat base on top of which lies the curf tracks.This track is then laid inside the former and the flat portion serves asan insulating layer between two coil layers while the tracks serve toalign the etched plates into their designed physical positions. In thisscheme, the plate structure is etched continuously without leaving tabsin the curfs. Although, the plate is not rigid when the etching isinitially finished, the positions are restored to their designed valuewhen placed on the alignment insulating mold as described above.

For the axial gradients, care should be taken to avoid leaving big areasof copper especially in the middle. Either these pieces are cut out orslits are etched in wide areas of copper patches to prevent theinduction of eddy currents from other gradients. To prevent a highresistance in the axial gradients, a thicker copper plate is preferablyused for the primary gradient while a thinner copper plate is preferablyused for the shield. For example, a 5 mm plate can be used for theprimary and a 3 mm plate for the shields. By this approach a reductionof resistance is gained compared to using thin copper plates in theprimary axial gradients as well.

This reduction in resistance is very significant because it means lessheat is generated and less power is needed to drive the coils. Thus thegradients produced by the present invention are stronger and switchfaster.

After the first gradient coil layer is put in place, a thin (typically0.5 mm) insulator layer is formed by a fiber cloth substrate and pottedwith epoxy after allowing it to settle. Then the next layer of thegradient coil can be placed atop the insulator layer. Subsequently,after another insulator layer, the third gradient coil is placed atopthe previous two. The gradient coil layers are potted by pouring epoxybetween the wire track etchings that are about 0.8 mm wide. To maintaina tight tolerance, generally about 0.1 mm variation across any surface,the plates are stacked in the former placed on a flat control surfacewith a tolerance of less than 0.1 mm, and a flat, heavy weight of thesame tolerance and control surface is applied during the epoxy curingprocess.

Because the gradient return loops need to run to the center of eachgradient coil these return tracks are created in between each semicirclefor the X and Y-gradient coils by exploiting their orthogonality. Forthe Z-gradient coil, the return track is either etched in the former ifit is the first layer or placed facing away from the gradients if it ison top. The only separations between gradient coil layers are theinsulation layers. This is a key step in the stacking efficiency. Forsuch a thin separation, the limit before exceeding the onset of coronaeffects is 50 kV/in voltage gradients. Thus, the insulation thicknesshas to be consistent with the amplifier drive voltages used. Thevoltages can vary anywhere from 100 to 500 or more volts so long as thevoltage divided by the separation between gradient layers is below 50kV/in.

The layers are placed in the former and relative to each other usingalignment pins during the placement of each layer. The alignment pinsdiffer in height and continue to grow as the layers are built up. Theflat weights have the corresponding holes to accommodate the alignmentholes during the curing process.

It is a fact that if the shield layers are placed directly on top of theprimary layers, then the fields produced in the imaging volume will benulled out. Consequently, the shield layers must be placed at somedistance away from the primary layers, preferably as far apart aspossible. Distancing the shield layers from the primaries is made easierby using etched plate technology with its high density stacking of wiretracks because of the ease in providing variable wire track widths andthus a better approximation of the theoretical design.

To obtain the most optimal stacking as called for by the performancespecification, all of the shim and cooling layers are placed in betweenthe primary layers and the shield layers with the exception of the 1storder shims because they will couple to the gradients. The 1st ordershims are placed on top of the shield layers. To make the shims ascompact as possible, they are designed by the same method using polarcoordinates and a radial envelope function to limit their planar extent.In addition, improved stacking efficiency can be obtained by etchingeach shim from a 0.1 to 0.5 mm thick insulated copper plate. Preferablythe shims have the same alignment holes as the other layers within thegradient coil. The shims are pre-processed to be self-insulated. Theshims can then be stacked atop each other and potted by an epoxy pourrunning through the etched tracks and a controlled surface weightapplied during the curing process. The surface weight is used forcompression and to maintain the flatness of the system, preferably towithin about 0.06 mm across the entire surface. If too much weight isused, the epoxy will be pushed out. If too little weight is used, thenthe layer buildup will be greater and the imaging region reduced beyondwhat was intended. Therefore, the weight of the compression plates isused to control the surface build up.

Cooling can be added to the gradient coils by any of several means. Oneapproach is to use channels in the layer between the primaries and theshields and then use air to cool the gradients. This method relies onconvective heat current elimination. A more efficient method is to usecopper tube with chilled water running through and using conductivecooling. The chilled water approach, however, generates eddy currents inthe copper tubes and requires the physical size of the tubes to be quitelarge. To avoid generating eddy currents, a zig-zag pattern or similarpatterns such as those shown in FIGS. 6 a and 6 b can be used. FIG. 6 brepresents a preferred pattern. To pack as much copper tubing betweenthe primary and shield layers as possible, the bending radius of thecopper tubes, r>=5×dia, can be exploited. A 3/16″ diameter copper tubeis sufficient for this purpose.

The cooling scheme of FIG. 6 b is preferred for a more even distributionof cold flow to hot flow between the incoming to outgoing flow.Furthermore, these tubes can be made of plastic as well and any patterncan be wound because they are not conductive and eddy currents will notbe induced. Moreover, instead of fluid, air-cooling can also be used toremove heat although it won't be as effective as using fluid. Yet evenfurther, instead of tubes just channels can be formed in the coolingspace and used for either fluid or air-cooling purposes without worryingabout inducing eddy currents.

The entire gradient coil layer, which contains the shims and cooling, ispotted together to form a very rigid unit. It has enough weight towithstand severe deformations or vibrations. Consequently, the pottingprocedure has the added advantage of suppressing acoustic noisegeneration resulting when the gradients are pulsed against the highstatic background field.

Wire interconnects are strategically place between the variousquadrants, top and bottom layers to give an extra degree of freedom inshunting current away from any quadrant for the delicate shieldingbalance required. This balance can be thrown off by manufacturingimperfections due to translational, rotational or vertical misplacementor offsets of the many gradient coil layers throughout. If this passivecorrection doesn't work, a final active correction can be appliedbecause of the symmetry of the gradients and shims. Pulses can beapplied to the shims when the gradients are turned on to provide afinal, almost perfect correction which will cancel any eddies and makethe shielded gradient coils work almost perfectly.

1. A method for designing a plurality of coil sets comprising planar Xand Y-primary coil sets and planar X and Y-shield coil sets of abi-planar gradient coil assembly said method comprising the steps of:specifying a surface primary and shield current distributions as well asa plurality of magnetic fields in polar coordinates and have reciprocalspace expressions related by a Fourier-Hankel transform; and obtaining asurface transverse primary and shield spatial current distributions thatgenerate a plurality of desired transverse gradient magnetic fields by:i. specifying polar surface current distributions on four coplanarplanes that share a common z-axis through their respective polar centersso the z-axis is in an orthogonal relation to the planes, setting thez-axis center equidistant between two inner planes so that these planesare positioned symmetrically at z=±a, then defining the currentdistributions on these planes as the primary coils where a plurality ofprimary gradient magnetic fields are generated therebetween; ii.specifying an outer plane to be positioned symmetrically at z=±b,defining the current distributions on these planes as the shield coilsso that a plurality of shield gradient magnetic fields are generated inopposition to the primary gradient magnetic fields, together producing atotal gradient magnetic field in the space between z<a and z>−a, andzero magnetic field in the space above z>b and below z<−b; iii. using ashielding condition of producing zero magnetic field in the space abovez>b and below z<−b to obtain an algebraic relation between the primaryand shield current distributions in reciprocal polar space; iv. usingthis primary and shield current distribution relation to express a totalshielded magnetic field in terms of just the primary currentdistribution; v. expressing the shielded gradient magnetic field in itsFourier-Hankel expansion so that a current density is in its reciprocalspace representation; vi. evaluating the magnetic field expression atspecified discrete values, these points all having a same axial positionz=c, where c<a, and a same polar angle φ, but different radial positionsρj, forming a term where for each j the magnetic field value soexpressed is subtracted from the desired magnetic field values at thatparticular jth location, then summing all these N terms where each termis multiplied by a different constant, the Lagrange multipliers, andthis sum added to an energy formula in its reciprocal spacerepresentation through a Fourier-Hankel expansion to finally yield anexpression which is an energy functional; vii. the energy functionaldifferentiated with respect to the current distribution and set to zero,subsequently solving the resultant expression to obtain an extremizedcurrent distribution in reciprocal space which becomes a sum over theLagrange multipliers multiplied by terms containing a plurality ofcorresponding radial constraint points; viii. the extremized currentdensity substituted back into the expression for the shielded gradientmagnetic field that will contain the sum over the N discrete radialpositions with the associated multiplicative Lagrange multipliers; ix.the field calculated at each discrete constraint value and set equal tothe corresponding constraint discrete magnetic field value to form amatrix equation of calculated field values at the discrete constraintradial positions times the corresponding Lagrange multipliers equalingthe constraint magnetic field values; x. inverting the matrix equationto finally obtain the Lagrange multipliers; xi. substituting theLagrange multiplier values in the expression for the extremized currentdensity; xii. the primary and shield magnetic fields calculated from theextremized current distribution by an inverse Fourier-Hankel transformto obtain the spatial field distributions, an efficiency and a linearityof the gradient magnetic fields so produced calculated, further aninductance also calculated from said current distribution; xiii. aparameter constructed as a figure of merit equal to the efficiencysquared and divided by the product of the inductance times thesquare-root of the linearity value; and xiv. optimizing the figure ofmerit by a Nelder-Mead simplex optimization algorithm that has anassociated cost function to limit the planar or radial extent of thecurrent distribution whereby in each iteration of the algorithm theextremized current distribution is obtained first, subsequently thefields, linearity and inductances calculated to get the figure of merit,then the radial constraint points with the associated magnetic fieldvalues varied by the simplex algorithm to obtain a new extremizedcurrent distribution from which to calculate a new figure of merit, thealgorithm terminating when no change is obtained in the figure of meritfinally yielding the desired transverse primary and shield currentdistributions.
 2. A method for designing the Z-primary coil and theZ-shield coil of the gradient coil assembly of claim 1, said methodfurther comprising the steps of: expanding an axial magnetic field interms of a Fourier-Hankel expansion, inverting this expression inreciprocal polar space so that a current density can be specified as afunction of the magnetic field; specifying two regions of constant axialmagnetic fields as a function of radial position on an interior planarsurface coaxial and parallel to a plurality of planar axial primarycurrent distributions; further specifying an outer axial magnetic fieldin opposite relation to the previous two axial magnetic fields to limita plurality of radial extents of the planar axial primary and shieldcurrent distributions; Fourier-Hankel transforming the fielddistributions and inputting them in said primary current distribution inreciprocal polar space; obtaining an associated planar axial shieldcurrent distribution from said primary current distribution andcalculating an interior axial shielded magnetic field from saidFourier-Hankel magnetic field expression so an efficiency and alinearity of the magnetic fields is found; further calculating acorresponding inductance from said planar axial primary and shieldcurrent distributions; forming a figure of merit by squaring theefficiency and dividing it by a product of the inductance and a squareroot of the linearity; optimizing the figure of merit by a Nelder-Meadsimplex optimization algorithm where the simplex algorithm varies arange and a plurality of amplitudes of the three target fielddistributions to obtain a new current distribution from which a newfigure of merit is obtained by calculating the corresponding axialshielded magnetic fields, and thus the efficiency and linearity, alongwith the inductance over each iteration, the algorithm terminating whenno change in the figure of merit is reached to yield an optimized planaraxial primary and shield current distribution.
 3. A method to define aplanar shim current distribution for a gradient coil assembly togenerate spatial magnetic field distributions corresponding to terms ina spherical harmonic expansion of a plurality of main magnetic fields,said method comprising the steps of: specifying polar, surface shimcurrent distributions placed on two parallel planes sharing a commonz-axis to produce a shim magnetic field there between; expressing theshim magnetic field in a Fourier-Hankel expansion, transforming the shimmagnetic fields to its reciprocal space representation, inverting theexpression so that the planar shim current distribution can be specifiedas a function of the shim magnetic field in reciprocal space; each termin the spherical harmonic expansion of the main magnetic field convertedto a plurality of cylindrical coordinates and multiplied by a radialenvelope function to constrain radial extent, then Fourier-Hankeltransformed to reciprocal space, the function entered as the shimmagnetic field in reciprocal field for the shim current distribution inreciprocal space; and the shim current distribution inverseFourier-Hankel transformed to obtain a continuous radial and angulardistribution in cylindrical coordinates.
 4. The planar currentdistributions solved for in claim 1 for the transverse, axial and shimcurrents being continuous surface distributions are discretized to formconductor placement positions wherein: if conductors of a samecross-sectional area are to be used, a continuous central conductor pathcan be obtained by constructing a plurality of corresponding streamfunctions and generating a plurality of contours of constant intervalsof an integrated current; if the continuous conductor paths are to beetched from a plurality of solid conductors the etch paths are formed inbetween said equal, constant intervals of integrated currents from thecorresponding stream functions.
 5. A method of manufacturing the coilsof claim 1, comprising the steps of: cutting a metal plate in the shapeof a circular coil creating a coil and a curf portion; removing the curfposition from the metal plate creating a curf void around the coil;placing a first insulation layer into the former; placing the coil intothe former over the first insulation layer; placing a second insulationlayer over the coil in the former; and compressing the insulating layersand the coil with a control weight.
 6. A method of manufacturing thecoils of claim 1, comprising the steps of: cutting a metal platecreating a noncontiguous curf portion and a coil with a plurality oftabs interconnecting sections of the coil; removing the curf portionfrom the metal plate creating a curf void around the coil; placing anepoxy into the curf void around coil; and removing the plurality of tabsfrom the coil.
 7. The method of claim 6, further comprising the stepsof: fabricating a former having an open top and a closed planar bottom;placing a first insulating layer inside the former and onto the formerplanar bottom; adhering the coil and epoxy onto the first insulatinglayer; adhering a second insulating layer on top of the coil and epoxy;and compressing the first and second insulating layers, the coil and theepoxy with a control weight.
 8. A method of manufacturing the coils ofclaim 1, comprising the steps of: cutting a metal plate in the shape ofa circular coil creating a coil portion and a curf portion; removing thecurf portion from the metal place creating a curf void round the coil;forming a formed insulation layer having curf tracks; and placing thecoil on the formed insulation between the curf tracks.
 9. The method ofclaim 8, further comprising the steps of: fabricating a former having anopen top and a closed planar bottom; placing the coil and the formedinsulation layer into the former; adhering a second insulating layer ontop of the coil and the formed insulation layer; and compressing thesecond insulating layer, the coil and the formed insulation layer with acontrol weight.
 10. A method of manufacturing a gradient coil assembly,comprising the steps of: fabricating a former having an open top and aclosed planar bottom; placing an insulation layer inside the former andonto the former planar bottom; fabricating and X-primary coil with acoil portion and a curf void portion; placing the X-primary coil intothe former; forming an insulation layer in the X-primary coil curf voidportion and on top of the X-primary coil portion; applying controlweight while the insulation layer cures; fabricating a Y-primary coilwith a coil portion and a curf void portion; placing the Y-primary coilinto the former; forming an insulation layer in the Y-primary coil curfvoid portion and on top of the Y-primary coil portion; applying controlweight while the insulation layer cures; fabricating a Z-primary coilwith a coil portion and a curf void portion; placing the Z-primary coilinto the former; forming an insulation layer in the Z-primary coil curfvoid portion and on top of the Z-primary coil portion; applying controlweight while the insulation layer cures; placing one or more coolingtubes on top of Z-primary coil portion and the insulation layer; pouringepoxy on top of and between cooling tubes forming an insulation layer;applying control weight while the insulation layer cures; placing a0^(th) and a 2^(nd) order shim on top of cooling tubes and theinsulation layer; pouring epoxy onto shims forming an insulation layer;applying control weight while the insulation layer cures; fabricating aZ-shield coil with a coil portion and a curf void portion; placing theZ-shield coil into the former; forming an insulation layer in theZ-shield coil curf void portion and on top of the Z-shield coil portion;applying control weight while the insulation layer cures; fabricating anX-shield coil with a coil portion and a curf void portion; placing theX-shield coil into the former; forming an insulation layer in theX-shield coil curf void portion and on top of the X-shield coil portion;applying control weight while the insulation layer cures; fabricating aY-shield coil with a coil portion and a curf void portion; placing theY-shield coil into the former; forming an insulation layer in theY-shield coil curf void portion and on top of the Y-shield coil portion;applying control weight while the insulation layer cures; placing 1^(st)order shims on top of Y-shield coil portion and insulation layer;pouring epoxy onto shim forming an insulation layer; applying controlweight while the insulation layer cures; and sealing the top of former.11. The method of claim 10, wherein the shims comprise self-insulatedcoils.
 12. The method of claim 10, wherein the former, the coils, theshims and the insulation layers have alignment holes to align theformer, the coils, the shims and the insulation layers relative to eachother.
 13. The method of claim 10, wherein the insulation layers consistof a fiber cloth substrate and epoxy.
 14. A gradient coil manufacturingmethod comprising in sequential order the steps of: i. fabricating apair of hollow cylindrical formers with a plurality of mounting holesplaced around an edge of the formers and a plurality of additionalmounting holes strategically placed in a central planar surface of theformers; ii. etching a X-primary coil from a solid copper plate by awater-jet cutting machine and placing the X-primary coil first on theformer using a plurality of pins through the central mounting holes thatextend vertically through all the layers to properly align the placementof the plate on the former; iii. placing a single layer of thin fibercloth on the X-primary coil and pouring an epoxy resin and a hardenermixture over it, then using a heavy, heated flat plate placed on top tohelp the epoxy resin settle forming an insulated layer and a flatcontrolled surface; iv. etching a Y-primary coil from a solid copperplate as in step ii and placing it in an orthogonal relation to theX-primary coil on top of the insulating layer using the aligning pins asin step ii; v. applying step iii to the Y-primary coil; vi. etching aZ-primary coil from a solid copper plate and placing it on top of theinsulating layer above the Y-primary coil using the aligning pins as instep ii; vii. applying step iii to the Z-primary coil; viii. placing aplurality of non-conducting cooling conduits on the insulating layerover the Z-primary coil then applying step iii; ix. subsequently,placing a preassembled set of shim layers comprising the zeroth andsecond order shims on top of the insulating layer above the coolinglayer then applying step iii to the shim layers; x. a layer made ofthick fiber cloth and a filler material mixed with the epoxy resin andthe hardener mixture over the cooling and insulating layer forms aninsulative support layer when step iii is applied to it to fill the gapbetween the shim and the shield layers; xi. an X-shield coil etched froma solid copper plate is placed on the support layer as in step ii,co-aligned with the X-primary coil, then step iii is applied to itafterwards; xii. a Y-shield coil etched from a solid copper plate andplaced in an orthogonal relation to the X-shield coil using step ii andsubsequently applying step iii to it forming an insulation layer; xiii.the Z-shield coil etched from a solid copper plate is placed on theinsulation layer above the Y-shield coil using step ii and subsequentlystep iii is applied to it to form an insulating layer; xiv. apreassembled set of shim layers comprising first, third and higher ordershim coils is placed on the insulating layer using step ii; and xv.applying step iii to the shim layer with additional fiber cloth layersforms a final insulative layer that caps the entire layer.
 15. Thegradient coil manufacturing method of claim 14, further comprising thestep of placing the central mounting holes strategically away from thedense parts of a plurality of current distributions throughout theentire shielded gradient coils to minimize disturbing the performance ofthe shielded coils and limit a gradient field leakage adjacent the polefaces.
 16. The gradient coil manufacturing method of claim 14, furthercomprising the step of placing a plurality of center fed busbars for theX and Y-primary and shield coils in the channels between the two halvesof each respective coil to save vertical stack up space.
 17. Thegradient coil manufacturing method of claim 14, further comprising thestep cutting a plurality of slits into a plurality of conductor tracksof the etched solid copper plates for the gradient coils.